1. Field of the Invention
The present invention relates to a decoding method and a decoder, more particularly to a cyclic code decoding method and a cyclic code decoder.
2. Description of the Related Art
Generally, a cyclic code is sent out by a transmitting end through a channel, and is received by a receiving end as a received sequence. The cyclic code has a plurality of symbols in a form of hard information (i.e., digital information, such as an integer), and the received sequence has a plurality of elements in a form of soft information (i.e., analog information, such as a floating number). Then, a conventional decoding method based on Chase algorithm is implemented at the receiving end. For example, D. Chase introduced a conventional decoding method in “A Class of Algorithms for Decoding Block Codes with Channel Measurement Information,” IEEE Trans. Inform. Theory, Vol. 18, No. 1, pages 170-182, Jan. 1972.
In the conventional decoding method, reliability of the elements of the received sequence is analyzed to obtain a plurality of evaluated codewords, and the evaluated codewords are decoded to obtain respective candidate codewords. Then, the candidate codewords are analyzed to determine one of those candidate codewords that is most similar to the received sequence, and said one of the candidate codewords is used as a decoded codeword of the received sequence. The Euclidean distance is commonly used to determine which one of the candidate codewords is most similar to the received sequence. However, since each of the elements of the received sequence is in a form of soft information and is expressed as a floating number, computations involved when determining the most similar one of the candidate codewords are complex.
In addition, a physical circuit for calculating an error location polynomial using Berlekamp-Massey algorithm or Euclidean algorithm is also complicated. Further, the conventional decoding method based on Chase algorithm requires a plurality of physical circuits for decoding the evaluated codewords to obtain the candidate codewords, respectively.